Velocity and Acceleration on a Rotating Disk?

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SUMMARY

The discussion focuses on calculating the velocity and acceleration of a person walking radially on a rotating disk with constant angular velocity. The linear velocity is determined using the formula v = ωr, where ω represents angular velocity and r is the radial distance from the center. The acceleration includes both centripetal acceleration and the component due to the person's walking speed, necessitating vector addition to accurately represent the total velocity and acceleration in two dimensions.

PREREQUISITES
  • Understanding of angular velocity (ω) and its relationship to linear velocity (v).
  • Knowledge of centripetal acceleration and its formula a = v²/r.
  • Familiarity with vector addition in two dimensions.
  • Basic principles of rotational motion and reference frames.
NEXT STEPS
  • Study the effects of angular velocity on linear motion in rotating frames.
  • Learn about vector calculus to differentiate velocity vectors for acceleration calculations.
  • Explore examples of non-inertial reference frames and their implications in physics.
  • Investigate the relationship between radial motion and centripetal force in rotating systems.
USEFUL FOR

Physics students, educators, and anyone interested in the dynamics of rotating systems and non-inertial reference frames.

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Homework Statement


If you are standing on a rotating disk which is rotating at a constant angular velocity and you walk with a speed v along a straight radial line, then what are you velocity and acceleration?


Homework Equations





The Attempt at a Solution


I just wanted to check if the linear velocity in this case will be:

v=w*r

and then the acceleration will just be the centripetal acceleration or am i understanding it wrong.
 
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The problem says that you're moving along a straight radial line - imagine that the disk has a straight line from the circumference to the centre, and, as the disk rotates, you start at the centre and walk along this line to the edge. If you were standing in one spot on the disk, then you would have v = r \omega and a = \frac{v^2}{r}, but in the situation described, there is an additional component. I think it should just be vector addition of velocities (in two dimensions), and acceleration would be found by differentiating the vector of velocity.
 
cheers. i get it now
 

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